def find_fixedpoints_normal(xmin=-10.0,
xmax=10.0,
xstep=1e-3,
alpha=-0.41769,
beta=-0.346251775,
plot=False):
no = NormalOscillator()
xrng = np.arange(xmin, xmax + xstep, xstep)
nullx = np.array([no.nullcline_x(xval, alpha, beta) for xval in xrng])
xp = zip(xrng, nullx, np.abs(nullx))
xp.sort(key=operator.itemgetter(-1))
top3 = np.array(xp[:3])
f = lambda x: no.nullcline_x(x, alpha, beta)
df = lambda x: no.nullcline_dx(x, alpha, beta)
zero_tol = 1e-6
x_tol = 1e-4
roots = list()
for k, xi in enumerate(top3[:, 0]):
try:
xz = newton(f, xi, fprime=df, maxiter=100)
except RuntimeError:
continue
xz_val = no.nullcline_x(xz, alpha, beta)
#print 'xz=%0.9f, xz_val=%0.9f' % (xz, xz_val)
if np.abs(xz_val) < zero_tol:
is_duplicate = False
for x, xv in roots:
if np.abs(x - xz) < x_tol:
is_duplicate = True
if not is_duplicate:
#print 'Root: x=%0.6f, f(x)=%0.6f' % (xz, xz_val)
roots.append([xz, xz_val])
roots = np.array(roots)
if plot:
plt.figure()
plt.plot(xrng, nullx, 'k-')
plt.plot(top3[:, 0], top3[:, 1], 'rx')
plt.plot(roots[:, 0], roots[:, 1], 'go')
plt.title('Fixed Point Surface for dv')
plt.xlabel('x')
plt.axis('tight')
return roots
